A boat capsized and sank in a lake. Based on an assumption of a mean weight of 138 ​lb, the boat was rated to carry 70 passengers​ (so the load limit was 9,660 ​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 138 lb to 172 lb. Complete parts a and b below. 3 Part Question... Part 1 A. Assume that a similar boat is loaded with 70 ​passengers, and assume that the weights of people are normally distributed with a mean of 178.1 lb and a standard deviation of 37.9 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 138 lb. The probability is (Blank). ​(Round to four decimal places as​ needed.)   Part 2   B. The boat was later rated to carry only 16 ​passengers, and the load limit was changed to 2,752 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 172 ​(so that their total weight is greater than the maximum capacity of 2,752 ​lb).   The probability is (Blank). ​(Round to four decimal places as​ needed.)   Part 3   C. Do the new ratings appear to be safe when the boat is loaded with 16 ​passengers? Choose the correct answer below.     A. Because 178.1 is greater than 172​, the new ratings do not appear to be safe when the boat is loaded with 16 passengers.   B. Because there is a high probability of​ overloading, the new ratings do not appear to be safe when the boat is loaded with 16 passengers.   C. Because there is a high probability of​ overloading, the new ratings appear to be safe when the boat is loaded with 16 passengers.   D. Because the probability of overloading is lower with the new ratings than with the old​ ratings, the new ratings appear to be safe.

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ISBN:9781119256830
Author:Amos Gilat
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A boat capsized and sank in a lake. Based on an assumption of a mean weight of 138 ​lb, the boat was rated to carry 70 passengers​ (so the load limit was 9,660 ​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 138 lb to 172 lb. Complete parts a and b below.

3 Part Question...

Part 1

A. Assume that a similar boat is loaded with 70 ​passengers, and assume that the weights of people are normally distributed with a mean of 178.1 lb and a standard deviation of 37.9 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 138 lb.
The probability is (Blank). ​(Round to four decimal places as​ needed.)
 
Part 2
 
B. The boat was later rated to carry only 16 ​passengers, and the load limit was changed to 2,752 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 172 ​(so that their total weight is greater than the maximum capacity of 2,752 ​lb).
 
The probability is (Blank).
​(Round to four decimal places as​ needed.)
 
Part 3
 
C. Do the new ratings appear to be safe when the boat is loaded with 16 ​passengers? Choose the correct answer below.
 
 
A. Because 178.1 is greater than 172​, the new ratings do not appear to be safe when the boat is loaded with 16 passengers.
 
B. Because there is a high probability of​ overloading, the new ratings do not appear to be safe when the boat is loaded with 16 passengers.
 
C. Because there is a high probability of​ overloading, the new ratings appear to be safe when the boat is loaded with 16 passengers.
 
D. Because the probability of overloading is lower with the new ratings than with the old​ ratings, the new ratings appear to be safe.
 
 
 
 
 
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